Regularized Lattice Boltzmann Research Articles

A regularized lattice Boltzmann method based on the multi-layer grid using a buffer scheme

The regularized lattice Boltzmann method (RLBM) has the advantage of improving the accuracy of numerical simulations without increasing the computational overhead. The RLBM usually uses the standard Cartesian grid in numerical simulation. This paper introduces the multi-layer grid technique, the multi-layer grid has different resolutions, which is also more consistent with the physical laws of the flow field. Based on this, a multi-layer grid regularized lattice Boltzmann method (ML-RLBM) for solving complex flow problems is proposed. The proposed method performs local refinement of the grid on the standard Cartesian grid to achieve a multi-layer grid, which can reduce the computational overhead. In order to realize the local grid refinement easily, this paper adopts the center point format to store the multi-layer grid. The ML-RLBM designs a buffer scheme between different layers of grids, which realizes that only spatial interpolation is required at the interface of different layers of grids without temporal interpolation. The numerical results show that the ML-RLBM has excellent numerical accuracy and numerical stability, and it can effectively reduce the computational cost.

Cooling effects of the derived coolant-film layer from partitioned porous injectors for transpiration cooling

This study aims to reveal the cooling benefits of the derived coolant film from partitioned porous injectors for transpiration cooling. The near-wall flow development and the cooling performance are investigated based on various layouts of porous injectors. The numerical investigation is conducted using an in-house recursive regularized thermal lattice Boltzmann method (RR-TLBM). The validated RR-TLBM solver is accelerated by three Tesla V100 graphic processing units (GPUs) for the simulation of incompressible and coupled-domain transpiration cooling at high Reynolds numbers, based on high-resolution grids with 2.65 × 108 nodes. The results indicate that the near-wall flow shows high momentum with the partitioned porous injectors. And the mean velocity increases by more than 23 % with the same coolant consumption per unit blowing area, which contributes to the coolant-film development and cooling uniformity downstream. Moreover, the partitioned porous layout shows the possibilities of coolant reduction as compared to the single continuous porous injector in Case 1. A reduction of 43 % in total coolant consumption with the partitioned porous layout only results in a decrease of 6 % in cooling performance downstream. Additionally, the partitioned coolant injection improves local cooling performance by roughly 22 %, with better cooling homogeneity at the same total coolant consumption. Turbulent fluctuations are weakened in the partitioned coolant injection zones, which contributes to an improvement in cooling evenness. The partitioned porous layout can be an appropriate choice for transpiration cooling systems.

Macroscopic finite-difference scheme based on the mesoscopic regularized lattice-Boltzmann method.

In this paper, we develop a macroscopic finite-difference scheme from the mesoscopic regularized lattice Boltzmann (RLB) method to solve the Navier-Stokes equations(NSEs) and convection-diffusion equation(CDE). Unlike the commonly used RLB method based on the evolution of a set of distribution functions, this macroscopic finite-difference scheme is constructed based on the hydrodynamic variables of NSEs (density, momentum, and strain rate tensor) or macroscopic variables of CDE (concentration and flux), and thus shares low memory requirement and high computational efficiency. Based on an accuracy analysis, it is shown that, the same as the mesoscopic RLB method, the macroscopic finite-difference scheme also has a second-order accuracy in space. In addition, we would like to point out that compared with the RLB method and its equivalent macroscopic numerical scheme, the present macroscopic finite-difference scheme is much simpler and more efficient since it is only a two-level system with macroscopic variables. Finally, we perform some simulations of several benchmark problems, and find that the numerical results are not only in agreement with analytical solutions, but also consistent with the theoretical analysis.

Numerical Analysis of Non-Newtonian Fluid Effects on the Equilibrium Position of a Suspended Particle and Relative Viscosity in Two-Dimensional Flow

A solvent in suspension often has non-Newtonian properties. To date, in order to determine these properties, many constitutive equations have been suggested. In particular, power-law fluid, which describes both dilatant and pseudoplastic fluids, has been used in many previous studies because of its simplicity. Then, the Herschel–Bulkley model is used, which describes fluid with yield stress. In this study, we considered how a non-Newtonian solvent affected the equilibrium position of a particle and relative viscosity using the regularized lattice Boltzmann method for fluid and a two-way coupling scheme for the particle. We focused on these methods so as to evaluate the non-Newtonian effects of a solvent. The equilibrium position in Bingham fluid was closer to the wall than that in Newtonian or power-law fluid. In contrast, the tendency of relative viscosity in Bingham fluid for each position was similar to that in power-law fluid.

Theoretical and numerical study on the well-balanced regularized lattice Boltzmann model for two-phase flow.

In the multiphase flow simulations based on the lattice Boltzmann equation(LBE), the spurious velocity near the interface and the inconsistent density properties are frequently observed. In this paper, a well-balanced regularized lattice Boltzmann (WB-RLB) model with Hermite expansion up to third order is developed for two-phase flows. To this end, the equilibrium distribution function and the modified force term proposed by Guo [Phys. Fluids 33, 031709 (2021)1070-663110.1063/5.0041446] are directly introduced into the regularization of the transformed distribution functions when considering the LBE with trapezoidal integral. First, to give a detailed comparison of the well-balanced lattice Boltzmann equation(WB-LBE), WB-RLB, and second-order mixed difference scheme (SOMDS) proposed by Lee and Fischer [Phys. Rev. E 74, 046709 (2006)1539-375510.1103/PhysRevE.74.046709], the theoretical analyses on the force balance of LBE with two different gradient operators, isotropic central scheme (ICS) and SOMDS, as well as the numerical simulations of the stationary droplet are carried out. The force analysis shows that SOMDS can achieve a higher accuracy than ICS for the force balance, which has been validated in the simulations of stationary droplet cases. For the stationary droplet cases, all three models (WB-LBE, WB-RLB, and SOMDS) can capture the physical equilibrium state even at a large density ratio of 1000. Also, the numerical investigations of the WB-RLB model with third-order expansion (WB-RLB3) demonstrate that adjusting the relaxation parameters of the third-order moment can further improve the accuracy and stability of the WB-RLB model. Then, both the droplet coalescence and the phase separation cases are investigated with considering the effect of different interface thickness, which demonstrates that the performance of the WB-RLB for the two-phase dynamic problems is still quite well, and it exhibits better numerical stability when compared with the WB-LBE. In addition, the contact angle problem is investigated by the present WB-RLB model; the numerical results show that the predicted values of the contact angles agree well with the analytical solutions, but the well-balance property is not validated, especially near the three-phase junction. Overall, the present WB-RLB model exhibits excellent numerical accuracy and stability for both static and dynamic interface problems.

A regularized lattice Boltzmann model with filter for multiphase flow with diffusion-dominated mass transfer considering two-film theory

Complex flow, considering the interfacial mass transfer with the two-film theory, is always encountered in critical industrial processes. The phase-field lattice Boltzmann method (PFLBM) coupling with the revised Fick's law mass transfer convection–diffusion equation (CDE) is a practical approach to predict the bulk concentration distribution in two-phase flows. However, solutions of concentration have oscillations and even diverge near the sharp gradient when the relaxation time of governing equations is close to 0.5 (i.e., diffusion-dominated). In this paper, an integrated PFLBM model considering two-phase flow and interfacial mass transfer with a new filtering algorithm and collision operator was built to extend the wider range of the existing model for the two-film CDE with an extremely low diffusion coefficient. First, the two-film mass transfer model from our team was furthermore developed with the second-order formation to meet the high precision of concentration on two-phase interfaces. Then, directional filtering algorithms and regularized-finite-difference (rLBM-FD) collision operator were introduced to improve the numerical stability and limit the numerical diffusion. Four common collision operators were implemented and thoroughly tested in two cases to verify the robustness and accuracy of our new model. In conclusion, the combination of the rLBM-FD with standard non-linear filter reaches the highest robustness, mass-conservativeness, and limitation on numerical diffusion. The directional non-linear filter has the lowest computational cost of any microscopic variable filter and can increase the robustness by two times. Macro-variable filtering is not appropriate for treating the two-film equilibrium because the mass loss and robustness are unacceptable.

Large-Scale Cluster Parallel Strategy for Regularized Lattice Boltzmann Method with Sub-Grid Scale Model in Large Eddy Simulation

As an improved method of the lattice Boltzmann method (LBM), the regularized lattice Boltzmann method (RLBM) has been widely used to simulate fluid flow. For solving high Reynolds number problems, large eddy simulation (LES) and RLBM can be combined. The computation of fluid flow problems often requires a large number of computational grids and large-scale parallel clusters. Therefore, the high scalability parallel algorithm of RLBM with LES on a large-scale cluster has been proposed in this paper. The proposed parallel algorithm can solve complex flow problems with large-scale Cartesian grids and high Reynolds numbers. In order to achieve computational load balancing, the domain decomposition method (DDM) has been used in large-scale mesh generation. Three mesh generation strategies are adopted, namely 1D, 2D and 3D. Then, the buffer on the grid interface is introduced and the corresponding 1D, 2D and 3D parallel data exchange strategies are proposed. For the 3D lid-driven cavity flow and incompressible flow around a sphere under a high Reynolds number, the given parallel algorithm is analyzed in detail. Experimental results show that the proposed parallel algorithm has a high scalability and accuracy on hundreds of thousands of cores.

Numerical modeling of fluid–structure–piezoelectric interaction for energy harvesting

In the present work, we propose a numerical coupling scheme combining the corotational Finite Element Method (FEM) for solid beams, the regularized Lattice Boltzmann Method (LBM) for fluid flows and a PiezoElectric Model (PEM) for energy harvesting module. The proposed coupling method can be employed to numerically solve Fluid–Structure–PiezoElectric Interaction (FSPEI) multiphysics problems which are the fundamental phenomena in the considered energy harvesting applications. In the proposed coupling method, the FEM and LBM are strongly coupled through the implicit Immersed Boundary Method (IBM) ensuring exactly the no-slip condition. Comparing with volumetric FEMs, the adopted corotational beam formulation can not only allow for large structural displacements, but also help improve the computational efficiency, as the solid structures for energy harvesting devices are usually slender under large motion. The piezoelectric effects are incorporated into the corotational beam dynamics with the help of the virtual work principle. The FEM, LBM and PEM are coupled together in a strong way in the sense that the time integrations are carried out without staggered communications. The proposed coupling scheme is assessed by a series of validation test-cases with increasing complexity, in which a good agreement is obtained with references.

On application of the regularized lattice Boltzmann method for isothermal flows with non-vanishing Knudsen numbers

Despite the advances in microscale modelling capabilities, physically observed non-zero Knudsen number (Kn) effects still elude the lattice Boltzmann method (LBM). This article details various Regularized LBM (RLBM) strategies used to model microscale flows and presents a thorough analysis on their applicability for the force-driven Poiseuille flow problem. In particular, we compare the formulations of eight schemes: Projected RLBM (P-RLBM), standard and Galilean Invariant Filtered Collision RLBM, Kn-dependant P-RLBM, Recursively Regularized LBM (R-RLBM), Hybrid R-RLBM, Central-Moment RLBM, and Onsager-Regularized LBM. We demonstrate, at different Kn with discrete Maxwell’s diffuse kinetic wall boundary conditions, the numerical equivalence of the considered RLBM schemes for hard sphere molecules on the D2Q9 lattice. Thereafter, we include a Kn-dependant wall-modified mean-free-path and extend the characterization onto higher-order D2Q17, D2Q21 and Q2Q25-Zero-One-Three, Q2Q49-Zero-One-Two-Three lattices. The study indicates that RLBM schemes are Navier-Stokes solvers which fail to entirely capture all the non-equilibrium phenomenon of slip/transition regime flows.

Pore-scale fluid flow and conjugate heat transfer study in high porosity Voronoi metal foams using multi-relaxation-time regularized lattice Boltzmann (MRT-RLB) method

This study aims to investigate pore-scale flow and conjugate heat transfer in high-porosity open-cell metal foams. Five representative elementary volume (REV) samples with different values of porosity (0.80, 0.85, and 0.90) and pore density (10, 20, and 30 PPI) are generated using the Laguerre-Voronoi tessellation (LVT) algorithm. To perform direct numerical simulations, a decoupled lattice Boltzmann solver is developed utilizing multi-relaxation-time (MRT) model for flow and regularized lattice Boltzmann (RLB) model for advection-diffusion. As a novelty, this solver is able to simulate advection-diffusion in the non-Darcy regime. To consider thermal conduction in REV samples more prominently, a constant high temperature is assigned to the solid ligaments on the inlet plane. The flow results show that the transition from the Darcy to the non-Darcy regime occurs at lower Reynolds numbers in foams with lower porosity, whereas the pore density does not affect the transition point significantly. According to the heat transfer results, metal foams cool down rapidly at high flow velocities while the temperature rise in the fluid is minimal. Also, increasing pore density from 10 PPI to 30 PPI and decreasing porosity from 0.90 to 0.80 increase the h-ReK slope in the non-Darcy regime by 190% and 17.5%, respectively.

Near-wall vortices and thermal simulation of coupled-domain transpiration cooling by a recursive regularized lattice Boltzmann method

The present study aims to reveal the near-wall vortices and the effects of flow states in coupled-domain transpiration cooling using a recursive regularized thermal lattice Boltzmann method (RR-TLBM). Large-eddy simulations of turbulent flow and heat transfer have been conducted on high-resolution computational grids using a desktop-level computer with CUDA 11.6. Results indicate that the near-wall flow structures present spatial characteristics along the streamwise direction. The vortex evolution promotes the downstream heat dissipation, even though turbulence impairs the effective cooling area. The spanwise evolvement of vortices strengthens the mixing of coolant and hot gas, and small-scale structures are beneficial for turbulent heat transfer. Moreover, the transition onset occurs earlier at higher Reynolds numbers, and it weakens the downstream cooling. The cooling performance of the derived coolant film is improved as the Reynolds number varies from 5 × 103 to 3 × 104 with a blowing ratio of F = 10%, whereas the local cooling is impaired at the high Reynolds numbers exceeding 5 × 104. The variation in flow states has little influence on the cooling performance at the Reynolds numbers larger than 3 × 106. On the other hand, our in-house RR-TLBM solver is highly stable and efficient for the simulation of flow and heat transfer with high Reynolds numbers. Simultaneously, a high computational performance of 1127 million lattices updated per second is achieved for our simulation of a coupled-domain turbulent flow and heat transfer, using the desktop-level computer with three Tesla V100 graphics processing units.

Comparative study of the virtual flux method and immersed boundary method coupled with regularized lattice Boltzmann method for suspension flow simulations

Suspension flows are ubiquitous in many fields, and reducing computational costs for numerical simulations of suspension flows remains a great challenge. Numerical simulations of particle-laden flows were performed here using the regularized lattice Boltzmann method (RLBM). RLBM, coupled with the virtual flux method (VFM) or the immersed boundary method (IBM) with the multi-direct forcing approach, conducted a series of three simulations for stationary and moving boundaries. The VFM and IBM results were compared for validation, and the computational efficiency was evaluated. For the two simulations using stationary and moving boundaries (i.e., a steady flow past a stationary cylinder and a plane Poiseuille flow including a single moving circular particle), the results based on the VFM and IBM were qualitatively comparable. The computational time for IBM was longer than that for VFM due to the iterations in its scheme. The pressure-driven suspension flow simulations showed that a dilute suspension's (<5%) relative viscosity was almost equivalent. The difference between the results obtained by the VFM and IBM in the semidilute regime (>10%) was discussed in terms of particle rotational motion. Even though the scalability for parallel computing was comparable between the VFM and IBM, the computational time could be effectively reduced by using the VFM instead of the IBM because of the increased suspension concentration.

Blade Dimension Optimization and Performance Analysis of the 2-D Ugrinsky Wind Turbine

With the increasing focus on renewable energy, there is a need to improve the efficiency of vertical-axis wind turbines (VAWTs). The Ugrinsky wind turbine is a type of VAWT, but there are few studies on this turbine. Previous studies have shown that the maximum power coefficient of the Ugrinsky wind turbine reaches 0.170, which is 54.5% higher than that of the Savonius type (0.110), and this turbine maintains a high power coefficient over a wide range of tip speed ratios (TSR). In this study, the dimensions of the two semicircles of the Ugrinsky wind turbine were further optimized to obtain a higher power coefficient. An analysis of the effect of the blade dimensions on the performance was conducted. The flow around the turbine was simulated using the regularized lattice Boltzmann method. The geometry of the turbine was simulated using the virtual flux method for the Cartesian grid. The optimization was conducted in terms of the output power coefficient and the average value of the power coefficient for neighboring TSR to consider the fluctuation of the TSR. This study demonstrates that a closer vortex distance favored the growth of the vortex and improved the power coefficient.

Propagation pattern for moment representation of the lattice Boltzmann method.

A propagation pattern for the moment representation of the regularized lattice Boltzmann method (LBM) in three dimensions is presented. Using effectively lossless compression, the simulation state is stored as a set of moments of the lattice Boltzmann distribution function, instead of the distribution function itself. An efficient cache-aware propagation pattern for this moment representation has the effect of substantially reducing both the storage and memory bandwidth required for LBM simulations. This paper extends recent work with the moment representation by expanding the performance analysis on central processing unit (CPU) architectures, considering how boundary conditions are implemented, and demonstrating the effectiveness of the moment representation on a graphics processing unit (GPU) architecture.

Regularized lattice Boltzmann method parallel model on heterogeneous platforms

AbstractAs an improved method of lattice Boltzmann method (LBM), regularized lattice Boltzmann method (RLBM) has been applied to simulate fluid flow. Nevertheless, the performance of RLBM needs to be considered when simulating actual problems. The rise of multicore platforms, especially the popularity of graphics processor units (GPUs), has provided possible implementation solutions for parallel computing. In this article, an RLBM parallel model on the CPU/GPU heterogeneous platforms is proposed. To solve the problem of possible GPU memory shortage, the CPU controls the startup of the kernel function in the RLBM algorithm and participates in the calculation. Due to the characteristics of the algorithm, the entire flow field is divided into CPU computing areas and GPU computing areas according to the given flow field division rules. OpenMP and CUDA are, respectively, applied to CPU and GPU for parallel computing. The startup of the kernel function takes a short time, and the CPU and GPU can be approximately regarded as performing calculations simultaneously. Since the data exchange between the CPU and GPU has a significant impact on performance, a buffer is set at the boundary of the CPU and GPU to reduce the frequency of data exchange. The buffer size determines the number of program iterations before exchanging data. The performance of the algorithm is measured by MFLUPS, and the algorithm is applied to the 3D lid‐driven cavity flow. The obtained results show that the MFLUPS of the algorithm is 25 times that of CPU MFLUPS, and it adds an increment equivalent to CPU MFLUPS compared with GPU MFLUPS. And the algorithm is extended to a multi‐GPU version, which is also applied to the 3D lid‐driven cavity flow. The results obtained show that the MFLUPS of the multi‐GPU version is 1.8 times that of the single GPU.

Onsager-regularized lattice Boltzmann method: A nonequilibrium thermodynamics-based regularized lattice Boltzmann method.

The regularized class of lattice Boltzmann methods (LBMs) leverage the potency of the standard lattice-Bhatnagar-Gross-Krook method by filtering out spurious nonhydrodynamic moments from the moment space; this is achieved through evaluating regularized populations via a multiscale or a Hermite polynomial expansion approach. In this paper, we propose an alternative approach for evaluating the lattice populations. This approach is based on a kinetic theory that is consistent with nonequilibrium thermodynamics and obeys the Onsager-reciprocity principle. The proposed method is verified and validated for a number of canonical problems such as the athermal shock tube, the double periodic shear layer, the lid driven cavity, flow past square cylinder, and Poiseuille flow at nonvanishing Knudsen numbers. Additionally, the proposed method is compared to existing regularized LBM schemes and is shown to yield significant improvement in the stability and accuracy of the simulations.

Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows

Rheological properties of the suspension flow, especially effective viscosity, partly depend on spatial arrangement and motion of suspended particles. It is important to consider effective viscosity from the microscopic point of view. For elliptical particles, the equilibrium position of inertial migration in confined state is unclear, and there are few studies on the relationship between dynamics of suspended particles and induced local effective viscosity distribution. Contribution of a single circular or elliptical particle flowing between parallel plates to the effective viscosity was studied, focusing on the particle–wall distance and particle rotational motion using the two-dimensional regularized lattice Boltzmann method and virtual flux method. As a result, confinement effects of the elliptical particle on the equilibrium position of inertial migration were summarized using three definitions of confinement. In addition, the effects of particle shape (aspect ratio and confinement) on the effective viscosity were assessed focusing on the particle–wall distance. The contribution of particle shape to the effective viscosity was found to be enhanced when the particle flowed near the wall. Focusing on the spatial and temporal variation of relative viscosity evaluated from wall shear stress, it was found that the spatial variation of the local relative viscosity was larger than temporal variation regardless of the aspect ratio and particle–wall distance.

A hybrid recursive regularized lattice Boltzmann model with overset grids for rotating geometries

Simulating rotating geometries in fluid flows for industrial applications remains a challenging task for general fluid solvers and in particular for the lattice Boltzmann method (LBM) due to inherent stability and accuracy problems. This work proposes an original method based on the widely used overset grids (or Chimera grids) while being integrated with a recent and optimized LBM collision operator, the hybrid recursive regularized model (HRR). The overset grids are used to actualize the rotating geometries where both the rotating and fixed meshes exist simultaneously. In the rotating mesh, the fictitious forces generated from its non-inertial rotating reference frame are taken into account by using a second order discrete forcing term. The fixed and rotating grids communicate with each other through the interpolation of the macroscopic variables. Meanwhile, the HRR collision model is selected to enhance the stability and accuracy properties of the LBM simulations by filtering out redundant higher order non-equilibrium tensors. The robustness of the overset HRR algorithm is assessed on different configurations, undergoing mid-to-high Reynolds number flows, and the method successfully demonstrates its robustness while exhibiting the second order accuracy.

Revisiting the Lattice Boltzmann Method Through a Nonequilibrium Thermodynamics Perspective

Abstract In this paper, we incorporate a nonequilibrium thermodynamics perspective that is consistent with the Onsager reciprocity principle into the lattice Boltzmann framework to propose a novel regularized lattice Boltzmann formulation for modeling the Navier–Stokes–Fourier equations. The new method is applied to one-dimensional (1D) isothermal situations wherein the advantages of incorporating such a nonequilibrium perspective can be explicitly appreciated. In such situations, the nonequilibrium contribution of the lattice populations obtained by the new method completely vanishes, and the lattice update is entirely reduced to evaluating the equilibrium distribution function. Such a counterintuitive 1D mesoscopic description is not obtained in any other existing lattice Boltzmann scheme. We therefore numerically test the proposed formulation on two complex problems, namely, shockwave and nonlinear wave propagation, and compare results with analytical results along with six existing lattice Boltzmann schemes; it is found that the new method indeed yields results that are more stable and accurate. These results highlight the potency of the nonequilibrium thermodynamics-based approach for obtaining accurate and stable lattice Boltzmann computations, and provide new insights into established lattice Boltzmann simulation methods.

Quantitative visualization and characteristics of gas flow in 3D pore-fracture system of tight rock based on Lattice Boltzmann simulation

The geometric complexity of the 3D pore-fracture system of tight rock at the pore-scale is a primary challenge for the prediction of gas flow. In this paper, the 3D pore-fracture systems of tight rock are reconstructed based on the representation unit volume (REV) of the intact tight sandstone and fractal fracture. A 3D regularized lattice Boltzmann model that considered the gas slippage effect is employed to simulate gas flow in the 3D pore-fracture systems. Effects of the micro-fracture morphology and gas rarefaction effect on gas flow and permeability of the pore-fracture systems are examined and investigated. The simulation results indicate that the gas flow behaviors in the pore-fracture system are strongly related to the above two factors. Gas flow behaviors in the pore-fracture structure is more sensitive at the low-pressure condition and gas rarefaction effect are more sensitive to the pore-fracture system with the highly rough fracture or the low fracture connectivity.